quadratisch gegen einen Wert streben

21:39 Jul 1, 2020
This question was closed without grading. Reason: Other

German to English translations [PRO]
Tech/Engineering - Automation & Robotics / conveyor belts / servo motors / automation
German term or phrase: quadratisch gegen einen Wert streben
Context:
Aufgrund der konstanten Beschleunigung a0 des Antriebs steigt die Geschwindigkeit linear bis zu ihrem Sollwert v0 an und bleibt dann zunächst konstant. Die Sollposition s des Antriebs steigt daher zunächst quadratisch an, im Bereich konstanter Geschwindigkeit dann nur noch linear. Nach Einsetzen des Bremsvorgangs (Beschleunigung -a0) fällt die Geschwindigkeit linear auf 0 und die Sollposition **strebt quadratisch gegen** ihren Endwert s0.

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To my knowledge, 'streben' in contexts like this is normally 'tends towards' a value. (e.g. strebt gegen Null/Unendlich). What does it mean here, and how do I deal with 'quadratisch'?
Something can increase or decrease quadratically, but can it tend quadratically towards...?

Maybe a poor choice of words by the author?

Anyone?

Thanks.
Cilian O'Tuama
Germany
Local time: 10:46


Summary of answers provided
4 +1converges on its final position S0 at a quadratic rate
Lancashireman
3 +1gravitate / edge in non-linear least squares towards an end-value
Adrian MM.
4tends quadratically towards
Andreea Sepi, MCIL (X)
Summary of reference entries provided
Quadratic convergence
Bernhard Sulzer

Discussion entries: 5





  

Answers


1 hr   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +1
strebt quadratisch gegen ihren Endwert s0.
converges on its final position S0 at a quadratic rate


Explanation:
I asked a mathematician, Cilian. Sometimes, you have to go beyond the talent pool on Kudoz.

Lancashireman
United Kingdom
Local time: 09:46
Native speaker of: Native in EnglishEnglish
PRO pts in category: 20
Notes to answerer
Asker: Many thanks Mr L, 'quadratic convergence' is actually an alternative I'm juggling with.


Peer comments on this answer (and responses from the answerer)
agree  Bernhard Sulzer: or "converges quadratically" see my reference
57 mins
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2 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5 peer agreement (net): +1
quadratisch gegen einen Endwert streben
gravitate / edge in non-linear least squares towards an end-value


Explanation:
I doubt this is anything to do with square roots or 'quadratic equations' from my school days last millennium, rather a parallel with linear / straight-line vs. reducing or declining balance 'squared' depreciation in accounting.

FWIW, I - having read works by a cousin once teaching at the technische Universität in Vienna - can't see anything wrong with the German, but maybe someone else can.

Example sentence(s):
  • ncremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics

    Reference: http://eng.proz.com/personal-glossaries/entry/2717023-kleins...
    Reference: http://www.roboticsproceedings.org/rss09/p42.pdf
Adrian MM.
Austria
Native speaker of: Native in EnglishEnglish
Notes to answerer
Asker: Hi Spaceman! :-) Yeah, 'sprachlich' the German appears fine, but 'inhaltlich'?


Peer comments on this answer (and responses from the answerer)
agree  Bernhard Sulzer: non-linear, gradual could also work, although I find nothing wrong with quadratic See my refs. "Ungleichmäßig" is also used in German; maybe moves /converges instead of gravitates, but I'll leave that up to others. / Cheers.
2 hrs
  -> Danke and thanks, Bernhard. Until Lancashireman's clever 'quadratic convergence', I had cogitated over moving and, to past ProZ Scan/Eng protests of Brit. Imperial inches & feet measurements, 'inching towards...'..
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14 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
tends quadratically towards


Explanation:
it's a standard mathematical phrase, just like "tends asymptotically to" (Calculus)
it moves towards that point in the fashion of a quadratic function (x to the power of 2).

I don't think there's much need to overthink this one. It appears like this in dozens of books, just see Google Books for instance.

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Note added at 1 day 8 hrs (2020-07-03 06:35:19 GMT)
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A Google search on my computer got 368.000 results. "Dozens" were just the books listed on the first results page, which include this exact phrase.
See for instance: Foundations of Computational Mathematics (Minneapolis, 2002) - page 122. Or Geometric Computations with Interval and New Robust Methods - page 50.

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Note added at 1 day 9 hrs (2020-07-03 06:53:01 GMT)
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Additional references: https://math.stackexchange.com/search?q=tend towards to

https://math.stackexchange.com/questions/1735193/in-practice...

So basically, they converge or tend (if a function has limits, it tends to the limits; else it converges)...

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Note added at 1 day 9 hrs (2020-07-03 07:03:11 GMT)
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http://sepwww.stanford.edu/public/docs/sep97/paul1/paper_htm...

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Note added at 1 day 16 hrs (2020-07-03 14:33:59 GMT)
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I typed "tends quadratically to". I admit I only looked at the first page. There I get a list of 6 books (GoogleBooks) that contain this exact phrase - they all deal with advanced mathematics of some kind. The remaining hits are probably due to the "tends to", which is quite common, so you are right, they are not relevant. I wish I could send you a screenshot. (It doesn't mean that my answer is correct, of course. My husband is an automotive engineer and he likes Lancashireman's answer best.)

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Note added at 1 day 17 hrs (2020-07-03 15:13:40 GMT)
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See also: http://www.netlib.org/utk/people/JackDongarra/PAPERS/Improvi...
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200...
https://arxiv.org/pdf/1704.06106.pdf (page 10)
https://core.ac.uk/download/pdf/25212689.pdf

Again, not sure if these apply to your specialism, but I have now double-checked and there are at least 4-5 results pages in Google for the phrase "tends quadratically to" (not towards!)



    Reference: http://https://books.google.de/books?id=3MQFkk12PBcC&pg=PA15...
    Reference: http://https://books.google.de/books?id=VLWkAgAAQBAJ&pg=PA50...
Andreea Sepi, MCIL (X)
Germany
Local time: 10:46
Native speaker of: Native in RomanianRomanian, Native in EnglishEnglish
Notes to answerer
Asker: Thanks Andreea. Your links don't appear to work."Dozens" isn't exactly a lot. Besides, I get only one single hit for the exact phrase, hence my doubts.

Asker: What EXACT term yielded 368,000 hits? It can't have been "tends quadratically towards" - as I say, that only gets 1-2 hits. Hardly convincing.


Peer comments on this answer (and responses from the answerer)
neutral  Chris Pr: Same answer as previously entered, albeit with a synonym swap....//Haha, well this is not economics, as we can see,,,and the 'Sollposition' is definitely not a function.... :))
11 hrs
  -> I studied Economics, and we never talked about functions gravitating or approaching. The standard phrase was "tend towards". Series converge; functions tend towards. If I remember correctly ;-)
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Reference comments


2 hrs peer agreement (net): +2
Reference: Quadratic convergence

Reference information:
https://bookdown.org/rdpeng/advstatcomp/rates-of-convergence...

Quadratic Convergence

Quadratic convergence is the fastest form of convergence that we will discuss here and is generally considered desirable if possible to achieve. We say the sequence converges at a quadratic rate if there exists some constant 0

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Note added at 2 hrs (2020-07-02 00:29:18 GMT)
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... Extending the examples from above, the sequence xn=1+(1n)2n converges quadratically to 1. ....

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Note added at 4 hrs (2020-07-02 01:48:15 GMT)
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ungleichmäßige versus lineare Beschleunigung:
https://studyflix.de/ingenieurwissenschaften/beschleunigung-...

gradual (quadratic) acceleration:
https://www.vexforum.com/t/gradual-quadratic-acceleration/22...

non-linear (quadratic) function:
https://ui.adsabs.harvard.edu/abs/2016EGUGA..1816816B/abstra...

It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series.

Bernhard Sulzer
United States
Native speaker of: German

Peer comments on this reference comment (and responses from the reference poster)
disagree  Chris Pr: The topic in question has nothing to do with "Advanced Statistical Computing"...//No complaint was made, just a statement of fact...
15 mins
  -> It has to to with "quadratischer" and "linearer Entwicklung." Those terms happen to be used in many areas. Not sure what you're complaining about. // OK. :)
agree  Adrian MM.
9 hrs
agree  Lancashireman
13 hrs
agree  Andreea Sepi, MCIL (X): I agree with "converge quadratically"
1 day 6 hrs
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